From esp Fri Dec 23 12:22:56 2005 Date: Fri, 23 Dec 2005 02:33:13 -0800 (PST) From: Sterl Phinney To: Scott A. Hughes Cc: Ryan Lang, Neil Cornish, Shane L. Larson, Tom Prince, Bonny L Schumaker Subject: 2Gm arm calculations Dear Scott, Ryan, Neil & Shane, Sterl Phinney's 23 Dec 2005 Official (see notes below) recommendations for "2Gm LISA" simulation sensitivity parameters: ----------------------------------------------------------------------- Recommended position error input to online Sensitivity curve calculator (whose input is 1-arm values, and output is sky-average, polarization average strain sensitivity in 1/rtHz): A. 9pm/rtHz (0.45 of default LISA value of 20pm/rtHz). This is approximately current best estimate of LISA performance, not allowing for Project's margins. *Do this case first, and if there is time for only one case of position noise. Project may howl at such a requirement, but LIST scientists think this is achievable. And only performance this good or better will avoid sacrificing most of LISA science with 2Gm arms. B. 15pm/rtHz (0.75 of default LISA value of 20pm/rtHz. This is 1/2 of the rss of 11Sep05 baseline allocations, except reducing the shot noise one by 2/5 (arm scaling of actual shot noise, so rss add to 15 instead of 20). *Do this second if time permits. Less likely to generate Project howls. For each of these two position noise cases, do 3 cases of acceleration noise: click on http://www.srl.caltech.edu/~shane/sensitivity/ .dat file generated with the above position noises, and then multiply the second column (COL2) as follows: f > 1e-4: hf = COL2 f < 1e-4: Option 0: accel noise \propto f^0 --> hf = COL2 [aka "White Optimistic"] Option 1: accel noise \propto f^{-0.5} --> hf = COL2 X (1e-4/f)^{0.5} [aka "Bender"] Option 2: accel noise \propto f^{-1.0} --> hf = COL2 X (1e-4/f) [aka "Vitale"] ------------------------------------------------------------------------- The foregoing are based on comments by Bonny Schumaker, Bill Folkner, Pete Bender, Karsten Danzmann, current LISA error budgets: LISAErrorBudget11Sep05.xls (in which numbers are Michelson 2-way, 2-arm values, i.e. pre-phase A position noise is 40pm/rtHz) and LISAErrorBudget15Dec05.xls (in which numbers are the "new standard" 1-way, 1-arm values, i.e. pre-phase A position noise is 20pm/rtHz) (both maintained by Tupper Hyde), and Phinney's study of the project spreadsheets. A's Motivation: this is obviously more stringent than the current baseline allocation, so could represent a cost increase. However, it is within reach of the current baseline "best estimates": 1/2 of LISAErrorBudget11Sep05.xls values (pm/rtHz) 5.6 shot (using 40cm optics, est. optical train efficiency epsilon=0.42) 6.6 path (pointing) 4.6 laser/clock/phasemeter 2.1 stray light ------ 10.0 (rss=root sum of squares 11Sep05 best estimate for 5Gm) All of the above are approx indep of arm length except for the shot noise, which scales as L, so if these "best estimates" are applied to the 2Gm arms, we would have "best estimate" 2.2 shot 7.6 path (pointing) 4.6 laser/clock/phasemeter 2.1 stray light ------- 8.6 (rss "11Sep05" best estimate for 2Gm) For reasons that aren't too clear to me, the more recent LISAErrorBudget15Dec05.xls has smaller best estimate numbers: 5.9 shot 2.8 path (pointing) [this went from exceeding its allocation of 13 [/2] in 11Sep05 to being only 2.8 of a new allocation of 4 in 15Dec05!? How!?] 3.5 laser/clock/phasemeter 0.9 stray light -------- 7.5 (rss 15Dec05 best estimate for 5Gm -why is Pete asking to relax the 5mHz strain sensitivity point then, with this a factor of 3 below!?) Scaling the shot only to 2Gm arms, we would have "best estimate" 2.4 shot 2.9 path (pointing) 3.5 laser/clock/phasemeter 0.9 stray light -------- 5.2 (rss "15Dec05" best estimate for 2Gm) So with inadequate (11Sep05) or adequate (15Dec05) margin, this makes 10pm/rtHz seem achievable for 2Gm arms.